Logical scalar, whether to scale the result to have a
maximum score of one. If no scaling is used then the result vector
has unit length in the Euclidean norm.
options
A named list, to override some ARPACK options. See
arpack for details.
Value
A named list with members:
vector
{The authority/hub scores of the vertices.}
valueThe corresponding eigenvalue of the calculated
principal eigenvector.
optionsSome information about the ARPACK computation, it has
the same members as the options member returned by
arpack, see that for documentation.
concept
Hub and authority score
Details
The authority scores of the vertices are defined as the principal
eigenvector of $A^T A$, where $A$ is the adjacency
matrix of the graph.
The hub scores of the vertices are defined as the principal
eigenvector of $A A^T$, where $A$ is the adjacency
matrix of the graph.
Obviously, for undirected matrices the adjacency matrix is symmetric
and the two scores are the same.
References
J. Kleinberg. Authoritative sources in a hyperlinked
environment. Proc. 9th ACM-SIAM Symposium on Discrete Algorithms,
1998. Extended version in Journal of the ACM 46(1999). Also
appears as IBM Research Report RJ 10076, May 1997.
See Also
evcent for eigenvector centrality,
page.rank for the Page Rank scores. arpack
for the underlining machinery of the computation.